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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 16PS

Textbook Problem

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Chebyshev’sEquation ConsiderChebyshev’s equation

Polynomial solutions of this differential equation are called Chebyshev polynomials and are denoted by T_{k}(x). They satisfy the recursion equation

Given that

Verify that

Verify the following Chebyshev polynomials.

**(a)**

To determine

**To calculate:** The value of Chebyshev polynomials

**Given information:** TheChebyshev’sequation

The recursion equation

**Calculation:**

Substitute

Now,

Substitute

Now,

**(b)**

To determine

**To prove:** That

**(c)**

To determine

**To prove:**

Multivariable Calculus

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Finding a General Solution Find the general...Ch. 16 - Distinct Real Zeros Given that the characteristic...Ch. 16 - Limit of a Solution Given that a and b are...Ch. 16 - Trivial and Nontrivial Solutions Consider the...Ch. 16 - Eulers Differential Equation Eulers differential...Ch. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Deflection of a Beam A horizontal beam with a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Airys Equation Consider Airys equation given in...Ch. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Bessels Equation: Order Zero The differential...Ch. 16 - Bessels Equation: Order One The differential...Ch. 16 - Hermites Equation Consider Hermites Equation...Ch. 16 - Laguerres Equation Consider Laguerres Equation...

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